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Signatures of non-homogeneous mixing in disease outbreaks. (English) Zbl 1145.92335
Summary: Despite their simplifying assumptions, simple SEIR (susceptible-exposed-infectious-removed)-type models for a homogeneously mixing fully susceptible population continue to provide useful insight and predictive capability. However, non-homogeneous mixing models such as those for outbreaks in social networks are often believed to provide better predictions of the benefits of various mitigation strategies such as isolation or vaccination. In practice, it is rarely known to what extent a SEIR-type model will adequately describe a given population. Therefore, our goal here is to evaluate possible retrospective signatures of non-homogeneous mixing or non-SEIR-type behavior. Each signature evaluated here is a measure of the goodness of fit of a SEIR-type model curve to the actual epidemic curve. For example, the extents of agreement between the final outbreak size and predictions of the final outbreak size based on reproduction number estimates arising from fitting various portions of the epidemic curve are possible signatures. On the basis of simulated outbreaks, we conclude that such signatures can detect non-SEIR-type behavior in some but not all of the social structures considered. The simulation study confirms that these signatures indicate non-SEIR-type behavior in a real 1918 influenza outbreak in Geneva.

MSC:
92D30 Epidemiology
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
Matlab; R
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[1] Anderson, R.M.; May, R.M., Infectious diseases of humans, (1991), Oxford University Press Oxford
[2] Barabási, A.-L.; Albert, R., Emergence of scaling in random networks, Science, 286, 509-512, (1999) · Zbl 1226.05223
[3] Brauer, F.; Castillo-Chavez, C., Mathematical models in population biology and epidemiology, (2000), Springer-Verlag New York · Zbl 1302.92001
[4] Britton, T., A test of homogeneity versus a specified heterogeneity in an epidemic model, Mathematical biosciences, 141, 79-99, (1997) · Zbl 0904.62122
[5] Burr, T.; Gattiker, J., The impact of model uncertainty on biological parameter estimates, Far east journal of theoretical statistics, 13, 2, 153-174, (2004) · Zbl 1068.62108
[6] Burr, T.; Chowell, G., Observation and model error effects on parameter estimates in susceptible – infected – recovered epidemic models, Far east journal of theoretical statistics, 19, 2, 163-183, (2006) · Zbl 1116.62118
[7] Centers for Disease Control and Prevention (CDC), Data from the CDC 122 Cities Mortality Reporting System as printed in Table III of the Morbidity and Mortality Weekly Report. Available on line at: http://wonder.cdc.gov/mmwr/mmwrmort.asp
[8] Chowell, G.; Fenimore, P.W.; Castillo-Garsow, M.A.; Castillo-Chavez, C., SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism, Journal of theoretical biology, 24, 1-8, (2003)
[9] Chowell, G.; Ammon, C.E.; Hengartner, N.W.; Hyman, J.M., Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions, Journal of theoretical biology, 241, 2, 193-204, (2006)
[10] Chowell, G.; Hyman, J.M.; Eubank, S.; Castillo-Chavez, C., Scaling laws for the movement of people between locations in a large city, Physical review E, 68, 066102, (2003)
[11] Colizza, V.; Barrat, A.; Barthelemy, M.; Vespignani, A., The modeling of global epidemics: stochastic dynamics and predictability, Bulletin of mathematical biology, 68, 1893-1921, (2006) · Zbl 1296.92225
[12] Dall, J.; Christensen, M., Random geometric graphs, Physical review E, 66, 016121, (2002)
[13] Drake, J.M., Limits to forecasting precision for outbreaks of directly transmitted diseases, Plos medicine, 3, 57-62, (2006)
[14] Gani, R.; Leach, S., Transmission potential of smallpox in contemporary populations, Nature, 414, 748-751, (2001)
[15] Hadeler, K.P.; Castillo-Chavez, C., A core group model for disease transmission, Mathematical biosciences, 128, 41-55, (1995) · Zbl 0832.92021
[16] Hethcote, H.W.; Yorke, J.A., (), 105 pages
[17] Hyman, J.M.; Li, J., Disease transmission models with biased partnership selection, Applied numerical mathematics, 24, 379-392, (1997) · Zbl 0878.92024
[18] Keeling, M.J.; Eames, K.T., Networks and epidemic models, Journal of the royal society interface, 2, 295-307, (2005)
[19] Kermack, W.O.; McKendrick, A.G., A contribution to the mathematical theory of epidemics, Proceedings of the royal society of London series A, 115, 700-721, (1927) · JFM 53.0517.01
[20] Kiss, I.Z.; Green, D.M.; Kao, R.R., The effect of contact heterogeneity and multiple routes of transmission on final epidemic size, Mathematical biosciences, 203, 124-136, (2006) · Zbl 1099.92063
[21] Liljeros, F.; Edling, C.R.; Nunes Amaral, L.A.; Stanley, H.E.; Aberg, Y., The web of human sexual contacts, Nature, 411, 907-908, (2001)
[22] Lipsitch, M.; Cohen, T.; Cooper, B., Transmission dynamics and control of severe acute respiratory syndrome, Science, 300, 1966-1970, (2003)
[23] Ludwig, D., Final size distributions for epidemics, Mathematical biosciences, 23, 33-46, (1975) · Zbl 0318.92025
[24] Ludwig, D.; Jones, D.D.; Holling, C.S., Qualitative analysis of insect outbreak systems: the spruce budworm and forest, The journal of animal ecology, 47, 315-322, (1978)
[25] S.A. Marion, C.E. Greenwood, Computation of the transient and final size distribution for an epidemic in a finite heterogeneous population. Abstract in: Conference on highly structured stochastic systems, Pavia, Italy, September 1999
[26] Ma, J.M.; Earn, D.J.D., Generality of the final size formula for an epidemic of a newly invading infectious disease, Bulletin of mathematical biology, 68, 679-702, (2006) · Zbl 1334.92419
[27] Matlab 7.3 for Linux. www.mathworks.com
[28] May, R.M.; Anderson, R.M., Spatial heterogeneity and the design of immunization programs, Mathematical biosciences, 72, 83-111, (1984) · Zbl 0564.92016
[29] Meyers, L.A.; Pourbohloul, B.; Newman, M.E.J.; Skowronski, D.M.; Brunham, R.C., Network theory and SARS: predicting outbreak diversity, Journal of theoretical biology, 232, 71-81, (2005)
[30] Newman, M.E.J., Coauthorship networks and patterns of scientific collaboration, Proceedings of the national Academy of sciences of the united states of America, 98, 404-409, (2001)
[31] Perelson, A.S.; Neumann, A.U.; Markowitz, M.; Leonard, J.M.; Ho, D.D., HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science, 271, 1582-1586, (1996)
[32] Press, W.; Flannery, B.; Teukolsky, S.; Vetterling, W., Numerical recipes, (1990), Cambridge University Press Cambridge · Zbl 0727.65001
[33] Sattenspiel, L.; Simon, C.P., The spread and persistence of infectious diseases in structured populations, Mathematical biosciences, 90, 341-366, (1988) · Zbl 0659.92013
[34] Splus for Windows version 7.0, 2005, Insightful Corporation
[35] Stroud, P.D.; Sydoriak, S.J.; Riese, J.M.; Smith, J.P.; Mniszewski, S.M.; Romero, P.R., Semi-empirical power-law scaling of new infection rate to model epidemic dynamics with inhomogeneous mixing, Mathematical biosciences, 203, 301-318, (2006) · Zbl 1101.92045
[36] Venables, W.; Ripley, B., Modern applied statistics with splus, (1999), Springer New York · Zbl 0927.62002
[37] Watts, D.J.; Strogatz, S., Collective dynamics of ‘small-world’ networks, Nature, 393, 440, (1998) · Zbl 1368.05139
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